{"id":"https://openalex.org/W2095865158","doi":"https://doi.org/10.1109/icassp.2011.5947214","title":"Using the kernel trick in compressive sensing: Accurate signal recovery from fewer measurements","display_name":"Using the kernel trick in compressive sensing: Accurate signal recovery from fewer measurements","publication_year":2011,"publication_date":"2011-05-01","ids":{"openalex":"https://openalex.org/W2095865158","doi":"https://doi.org/10.1109/icassp.2011.5947214","mag":"2095865158"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2011.5947214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5947214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079958889","display_name":"Hanchao Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hanchao Qi","raw_affiliation_strings":["Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, USA","Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, USA#TAB#","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102132389","display_name":"Shannon M. Hughes","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shannon Hughes","raw_affiliation_strings":["Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, USA","Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, USA#TAB#","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079958889"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":4.5788,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.94937391,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3940","last_page":"3943"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.688337504863739},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6040716171264648},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6012108325958252},{"id":"https://openalex.org/keywords/signal-recovery","display_name":"Signal recovery","score":0.5863410234451294},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.5575495958328247},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3595767021179199},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3471341133117676},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3286609649658203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23388847708702087}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.688337504863739},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6040716171264648},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6012108325958252},{"id":"https://openalex.org/C2989281035","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Signal recovery","level":3,"score":0.5863410234451294},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.5575495958328247},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3595767021179199},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3471341133117676},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3286609649658203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23388847708702087},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/icassp.2011.5947214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5947214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.309.2754","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.2754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ecee.colorado.edu/~smhughes/QiHughesKernelTrickinCompressiveSensing.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.895.6178","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.895.6178","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mirlab.org/conference_papers/International_Conference/ICASSP%202011/pdfs/0003940.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1560724230","https://openalex.org/W1587559447","https://openalex.org/W2018233872","https://openalex.org/W2104339857","https://openalex.org/W2119667497","https://openalex.org/W2133396101","https://openalex.org/W2296616510","https://openalex.org/W3144619878","https://openalex.org/W3195149063","https://openalex.org/W4250955649","https://openalex.org/W4313169793","https://openalex.org/W6634974784"],"related_works":["https://openalex.org/W1502442302","https://openalex.org/W2537887767","https://openalex.org/W2087326866","https://openalex.org/W2118132594","https://openalex.org/W2078389543","https://openalex.org/W3024569604","https://openalex.org/W2136676913","https://openalex.org/W3029251452","https://openalex.org/W3040759966","https://openalex.org/W2950736325"],"abstract_inverted_index":{"Compressive":[0],"sensing":[1,73,183],"accurately":[2,133],"reconstructs":[3],"a":[4,75,82,95,106],"signal":[5,40,83,90,214],"that":[6,103,122,171],"is":[7,30,47,144,215],"sparse":[8],"in":[9,67,160],"some":[10],"basis":[11,163],"from":[12,42,139],"measurements,":[13,142,184],"generally":[14],"consisting":[15],"of":[16,27,35,78,98,112,115,151,158,181,192,199,211],"the":[17,33,36,50,63,89,149,156,187,193,209],"signal's":[18],"inner":[19],"products":[20],"with":[21,203],"Gaussian":[22],"random":[23],"vectors.":[24],"The":[25],"number":[26,150],"measurements":[28,45,152],"needed":[29],"based":[31],"on":[32,208],"sparsity":[34,159],"signal,":[37],"allowing":[38],"for":[39,178],"recovery":[41],"far":[43,146,176],"fewer":[44],"than":[46,148],"required":[48,154],"by":[49,196],"traditional":[51],"Shannon":[52],"sampling":[53],"theorem.":[54],"In":[55,166],"this":[56,113],"paper,":[57],"we":[58,169,172],"show":[59,130],"how":[60,131],"to":[61,70,74,84,132],"apply":[62],"kernel":[64],"trick,":[65],"popular":[66],"machine":[68],"learning,":[69],"adapt":[71],"compressive":[72,182],"different":[76],"type":[77,114],"sparsity.":[79,117],"We":[80,129],"consider":[81],"be":[85,92],"\u201cnonlinearly":[86],"K-sparse\u201d":[87],"if":[88],"can":[91,173],"recovered":[93,194,213],"as":[94,126],"nonlinear":[96,116],"function":[97],"K":[99],"underlying":[100],"parameters.":[101],"Images":[102],"lie":[104],"along":[105],"low-dimensional":[107],"manifold":[108],"are":[109,125],"good":[110],"examples":[111],"It":[118],"has":[119],"been":[120],"shown":[121],"natural":[123],"images":[124,175],"well":[127],"[1].":[128],"recover":[134,174],"these":[135],"nonlinearly":[136],"K-sparse":[137],"signals":[138],"approximately":[140],"2K":[141],"which":[143],"often":[145],"lower":[147],"usually":[153],"under":[155],"assumption":[157],"an":[161,197],"orthonormal":[162],"(e.g.":[164],"wavelets).":[165],"experimental":[167],"results,":[168],"find":[170],"better":[177],"small":[179],"numbers":[180],"sometimes":[185],"reducing":[186],"mean":[188],"square":[189],"error":[190,210],"(MSE)":[191],"image":[195],"order":[198],"magnitude":[200],"or":[201],"more,":[202],"little":[204],"computation.":[205],"A":[206],"bound":[207],"our":[212],"also":[216],"proved.":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}